a) Yes, it is right.b) Once I have looked for the puzzle I almost immediatly spoted the AUR, constructed mentaly the link from "2" to "9", and then I started the construction of links from the "9" (and not from the "2", because there is in the same unit of r1c3 a bivalue node with "9", whereas that doesn't happen for "2").c) The nice loop notation its just that: a notation. More important is to visualize the implications of the loop in the puzzle and see by ourselves that r7c2 must really be "2". Also, it is very important to confirm the deduction of a loop by looking to the puzzle.

This one was certainly much tougher than I thought it was going to be and I think nigh on impossible on paper i.e. without a programme to highlight particular candidate numbers and colouring facility. This was how I managed it eventually:

First, thanks for the puzzle you have posted. Second, I want to congratulate you for this very good and interesting puzzle, where some advanced techniques can be applied. My solution have 9 steps, and, personaly, I rate it just a little easier than exercise #5. Clearly, your generator is getting better and better. Keep the good work.

Does this personalized cycle notation correctly describe Carcul's loop? I like including the links inside the cells/nodes so that I can better keep track of what is going on. The (5&7) is a grouping that is true only when both 5 and 7 are true in the node. Since the 2 in r7c2 is a discontinuity connected by strong links, it must be true!?

Interesting aside, I don't think you can count an AUR strong link as a nominal link, because r7c2 = 2 would not in general imply that r1c3 <> 9

Myth Jellies wrote:I don't think you can count an AUR strong link as a nominal link, because r7c2 = 2 would not in general imply that r1c3 <> 9

First, I don't know what a "nominal link" is. Perhaps you could first explain your own terms when they differ from the commonly used ones. Second, I have never said that the link in an AUR is a strong one: if you read carefully the post about AURs, you will read that the "link is similar but not completely equivalent to the type of link that exists in an ALS having two of his values in just one cell each." So, I don't understand why r7c2=2 would imply r1c3<>9.

Myth Jellies wrote:Since the 2 in r7c2 is a discontinuity connected by strong links, it must be true!?

Instead of trying to understand your notation, or mine, why don't you make r7c2<>2 and see what happen? Also, in terms of the traditional nice loop rules, r7c2 is a discontinuity with one strong link and two weak links with different labels from the one of the strong link, and so the labels of the weak links can be eliminated from this node, leaving "2" as the only possible value for r7c2.